Pioneering papers [1]}, [2]} are based on the above-outlined kinetic framework.
Their remarkable contribution (an adjustable element) was to apply phase shift outputs of the self-consistent procedure of auxiliary-orbital-based (Kohn-Sham) DFT for screening of an embedded bare charge \(Z_1\) , independently of incoming-ion charge states. In such a buildup-procedure of complete screening, where we respect the impact of a metallic medium in all one-electron states
a priori, one has the Friedel sum rule of neutrality with charge \(Q\) 
on [3]} impurity
\(Q\equiv {Z_1}\, =\, \frac{2}{\pi }\, \sum _{l=0}^{\infty }\, (2l+1)\, \delta _l(v_F),\) 
